Finance McGraw−Hill Primis ISBN: 0−390−32002−1 Text: Investments, Fifth Edition Bodie−Kane−Marcus Course: Investments Instructor: David Whitehurst UMIST Volume 2 McGraw-Hill/Irwin abc Finance http://www.mhhe.com/primis/online/ Copyright ©2003 by The McGraw−Hill Companies, Inc. All rights reserved. Printed in the United States of America. Except as permitted under the United States Copyright Act of 1976, no part of this publication may be reproduced or distributed in any form or by any means, or stored in a database or retrieval system, without prior written permission of the publisher. This McGraw−Hill Primis text may include materials submitted to McGraw−Hill for publication by the instructor of this course. The instructor is solely responsible for the editorial content of such materials. 111 FINA ISBN: 0−390−32002−1 This book was printed on recycled paper. Finance Volume 2 Bodie−Kane−Marcus • Investments, Fifth Edition VII. Active Portfolio Management 919 27. The Theory of Active Portfolio Management 919 Back Matter 942 Appendix A: Quantitative Review 942 Appendix B: References to CFA Questions 978 Glossary 980 Name Index 992 Subject Index 996 iii Bodie−Kane−Marcus: Investments, Fifth Edition VII. Active Portfolio Management 27. The Theory of Active Portfolio Management 919 © The McGraw−Hill Companies, 2001 CHAPTER TWENTY–SEVEN THE THEORY OF ACTIVE PORTFOLIO MANAGEMENT Thus far we have alluded to active portfolio management in only three instances: the Markowitz methodology of generating the optimal risky portfolio (Chapter 8); security analysis that generates forecasts to use as inputs with the Markowitz pro- cedure (Chapters 17 through 19); and fixed-income portfolio management (Chap- ter 16). These brief analyses are not adequate to guide investment managers in a comprehensive enterprise of active portfolio management. You may also be won- dering about the seeming contradiction between our equilibrium analysis in Part III—in particular, the theory of ef- ficient markets—and the real-world environment where profit-seeking in- vestment managers use active manage- ment to exploit perceived market inefficiencies. Despite the efficient market hypoth- esis, it is clear that markets cannot be perfectly efficient; hence there are rea- sons to believe that active management can have effective results, and we dis- cuss these at the outset. Next we con- sider the objectives of active portfolio management. We analyze two forms of active management: market timing, which is based solely on macroeconomic factors; and security selection, which in- cludes microeconomic forecasting. We show the use of multifactor models in ac- tive portfolio management, and we end with a discussion of the use of imperfect forecasts and the implementation of security analysis in industry. 916 Bodie−Kane−Marcus: Investments, Fifth Edition VII. Active Portfolio Management 27. The Theory of Active Portfolio Management 920 © The McGraw−Hill Companies, 2001 CHAPTER 27 The Theory of Active Portfolio Management 917 27.1 THE LURE OF ACTIVE MANAGEMENT How can a theory of active portfolio management be reconciled with the notion that mar- kets are in equilibrium? You may want to look back at the analysis in Chapter 12, but we can interpret our conclusions as follows. Market efficiency prevails when many investors are willing to depart from maximum diversification, or a passive strategy, by adding mispriced securities to their portfolios in the hope of realizing abnormal returns. The competition for such returns ensures that prices will be near their “fair” values. Most managers will not beat the passive strategy on a risk- adjusted basis. However, in the competition for rewards to investing, exceptional managers might beat the average forecasts built into market prices. There is both economic logic and some empirical evidence to indicate that exceptional portfolio managers can beat the average forecast. Let us discuss economic logic first. We must assume that if no analyst can beat the passive strategy, investors will be smart enough to divert their funds from strategies entailing expensive analysis to less expensive passive strategies. In that case funds under active management will dry up, and prices will no longer reflect sophisticated forecasts. The consequent profit opportunities will lure back ac- tive managers who once again will become successful. 1 Of course, the critical assumption is that investors allocate management funds wisely. Direct evidence on that has yet to be produced. As for empirical evidence, consider the following: (1) Some portfolio managers have produced streaks of abnormal returns that are hard to label as lucky outcomes; (2) the “noise” in realized rates is enough to prevent us from rejecting outright the hypothesis that some money managers have beaten the passive strategy by a statistically small, yet eco- nomically significant, margin; and (3) some anomalies in realized returns have been suffi- ciently persistent to suggest that portfolio managers who identified them in a timely fashion could have beaten the passive strategy over prolonged periods. These conclusions persuade us that there is a role for a theory of active portfolio man- agement. Active management has an inevitable lure even if investors agree that security markets are nearly efficient. Suppose that capital markets are perfectly efficient, that an easily accessible market- index portfolio is available, and that this portfolio is for all practical purposes the efficient risky portfolio. Clearly, in this case security selection would be a futile endeavor. You would be better off with a passive strategy of allocating funds to a money market fund (the safe asset) and the market-index portfolio. Under these simplifying assumptions the opti- mal investment strategy seems to require no effort or know-how. Such a conclusion, however, is too hasty. Recall that the proper allocation of investment funds to the risk-free and risky portfolios requires some analysis because y, the fraction to be invested in the risky market portfolio, M, is given by (27.1) where E(r M ) – r f is the risk premium on M, ␴ 2 M its variance, and A is the investor’s coeffi- cient of risk aversion. Any rational allocation therefore requires an estimate of ␴ M and E(r M ). Even a passive investor needs to do some forecasting, in other words. Forecasting E(r M ) and ␴ M is further complicated by the existence of security classes that are affected by different environmental factors. Long-term bond returns, for example, are y ϭ E(r M ) Ϫ r f .01A␴ 2 M 1 This point is worked out fully in Sanford J. Grossman and Joseph E. Stiglitz, “On the Impossibility of Informationally Efficient Markets,” American Econonic Review 70 (June 1980). Bodie−Kane−Marcus: Investments, Fifth Edition VII. Active Portfolio Management 27. The Theory of Active Portfolio Management 921 © The McGraw−Hill Companies, 2001 driven largely by changes in the term structure of interest rates, whereas equity returns de- pend on changes in the broader economic environment, including macroeconomic factors beyond interest rates. Once our investor determines relevant forecasts for separate sorts of investments, she might as well use an optimization program to determine the proper mix for the portfolio. It is easy to see how the investor may be lured away from a purely passive strategy, and we have not even considered temptations such as international stock and bond portfolios or sector portfolios. In fact, even the definition of a “purely passive strategy” is problematic, because simple strategies involving only the market-index portfolio and risk-free assets now seem to call for market analysis. For our purposes we define purely passive strategies as those that use only index funds and weight those funds by fixed proportions that do not vary in response to perceived market conditions. For example, a portfolio strategy that always places 60% in a stock market–index fund, 30% in a bond-index fund, and 10% in a money market fund is a purely passive strategy. More important, the lure into active management may be extremely strong because the potential profit from active strategies is enormous. At the same time, competition among the multitude of active managers creates the force driving market prices to near efficiency levels. Although enormous profits may be increasingly difficult to earn, decent profits to the better analysts should be the rule rather than the exception. For prices to remain effi- cient to some degree, some analysts must be able to eke out a reasonable profit. Absence of profits would decimate the active investment management industry, eventually allow- ing prices to stray from informationally efficient levels. The theory of managing active portfolios is the concern of this chapter. 27.2 OBJECTIVES OF ACTIVE PORTFOLIOS What does an investor expect from a professional portfolio manager, and how does this ex- pectation affect the operation of the manager? If the client were risk neutral, that is, indif- ferent to risk, the answer would be straightforward. The investor would expect the portfolio manager to construct a portfolio with the highest possible expected rate of return. The port- folio manager follows this dictum and is judged by the realized average rate of return. When the client is risk averse, the answer is more difficult. Without a normative theory of portfolio management, the manager would have to consult each client before making any portfolio decision in order to ascertain that reward (average return) is commensurate with risk. Massive and constant input would be needed from the client-investors, and the economic value of professional management would be questionable. Fortunately, the theory of mean-variance efficient portfolio management allows us to separate the “product decision,” which is how to construct a mean-variance efficient risky portfolio, and the “consumption decision,” or the investor’s allocation of funds between the efficient risky portfolio and the safe asset. We have seen that construction of the optimal risky portfolio is purely a technical problem, resulting in a single optimal risky portfolio appropriate for all investors. Investors will differ only in how they apportion investment to that risky portfolio and the safe asset. Another feature of the mean-variance theory that affects portfolio management deci- sions is the criterion for choosing the optimal risky portfolio. In Chapter 8 we established that the optimal risky portfolio for any investor is the one that maximizes the reward-to- variability ratio, or the expected excess rate of return (over the risk-free rate) divided by the standard deviation. A manager who uses this Markowitz methodology to construct the op- timal risky portfolio will satisfy all clients regardless of risk aversion. Clients, for their part, 918 PART VII Active Portfolio Management Bodie−Kane−Marcus: Investments, Fifth Edition VII. Active Portfolio Management 27. The Theory of Active Portfolio Management 922 © The McGraw−Hill Companies, 2001 CHAPTER 27 The Theory of Active Portfolio Management 919 can evaluate managers using statistical methods to draw inferences from realized rates of return about prospective, or ex-ante, reward-to-variability ratios. William Sharpe’s assessment of mutual fund performance 2 is the seminal work in the area of portfolio performance evaluation (see Chapter 24). The reward-to-variability ratio has come to be known as Sharpe’s measure: It is now a common criterion for tracking performance of professionally managed portfolios. Briefly, mean-variance portfolio theory implies that the objective of professional port- folio managers is to maximize the (ex-ante) Sharpe measure, which entails maximizing the slope of the CAL (capital allocation line). A “good” manager is one whose CAL is steeper than the CAL representing the passive strategy of holding a market-index portfolio. Clients can observe rates of return and compute the realized Sharpe measure (the ex-post CAL) to evaluate the relative performance of their manager. Ideally, clients would like to invest their funds with the most able manager, one who consistently obtains the highest Sharpe measure and presumably has real forecasting abil- ity. This is true for all clients regardless of their degree of risk aversion. At the same time, each client must decide what fraction of investment funds to allocate to this manager, plac- ing the remainder in a safe fund. If the manager’s Sharpe measure is constant over time (and can be estimated by clients), the investor can compute the optimal fraction to be in- vested with the manager from equation 27.1, based on the portfolio long-term average re- turn and variance. The remainder will be invested in a money market fund. The manager’s ex-ante Sharpe measure from updated forecasts will be constantly vary- ing. Clients would have liked to increase their allocation to the risky portfolio when the forecasts are optimistic, and vice versa. However, it would be impractical to constantly communicate updated forecasts to clients and for them to constantly revise their allocation between the risky portfolios and risk-free asset. Allowing managers to shift funds between their optimal risky portfolio and a safe asset according to their forecasts alleviates the problem. Indeed, many stock funds allow the managers reasonable flexibility to do just that. 27.3 MARKET TIMING Consider the results of the following two different investment strategies: 1. An investor who put $1,000 in 30-day commercial paper on January 1, 1927, and rolled over all proceeds into 30-day paper (or into 30-day T-bills after they were introduced) would have ended on December 31, 1978, fifty-two years later, with $3,600. 2. An investor who put $1,000 in the NYSE index on January 1, 1927, and reinvested all dividends in that portfolio would have ended on December 31, 1978, with $67,500. Suppose we defined perfect market timing as the ability to tell (with certainty) at the beginning of each month whether the NYSE portfolio will outperform the 30-day paper portfolio. Accordingly, at the beginning of each month, the market timer shifts all funds S ϭ E(r P ) Ϫ r f ␴ P 2 William F. Sharpe, “Mutual Fund Performance,” Journal of Business, Supplement on Security Prices 39 (January 1966). Bodie−Kane−Marcus: Investments, Fifth Edition VII. Active Portfolio Management 27. The Theory of Active Portfolio Management 923 © The McGraw−Hill Companies, 2001 into either cash equivalents (30-day paper) or equities (the NYSE portfolio), whichever is predicted to do better. Beginning with $1,000 on the same date, how would the perfect timer have ended up 52 years later? This is how Nobel Laureate Robert Merton began a seminar with finance professors 20 years ago. As he collected responses, the boldest guess was a few million dollars. The cor- rect answer: $5.36 billion. 3 These numbers highlight the power of compounding. This effect is particularly impor- tant because more and more of the funds under management represent retirement savings. The horizons of such investments may not be as long as 52 years but are measured in decades, making compounding a significant factor. Another result that may seem surprising at first is the huge difference between the end-of- period value of the all-safe asset strategy ($3,600) and that of the all-equity strategy ($67,500). Why would anyone invest in safe assets given this historical record? If you have internalized the lessons of previous chapters, you know the reason: risk. The average rates of return and the standard deviations on the all-bills and all-equity strategies for this period are: Arithmetic Mean Standard Deviation Bills 2.55 2.10 Equities 10.70 22.14 The significantly higher standard deviation of the rate of return on the equity portfolio is commensurate with its significantly higher average return. Can we also view the rate-of-return premium on the perfect-timing fund as a risk pre- mium? The answer must be “no,” because the perfect timer never does worse than either bills or the market. The extra return is not compensation for the possibility of poor returns but is attributable to superior analysis. It is the value of superior information that is re- flected in the tremendous end-of-period value of the portfolio. The monthly rate-of-return statistics for the all-equity portfolio and the timing portfolio are: All Perfect Timer Perfect Timer Equities No Charge Fair Charge Per Month (%) (%) (%) Average rate of return 0.85 2.58 0.55 Average excess return over return on safe asset 0.64 2.37 0.34 Standard deviation 5.89 3.82 3.55 Highest return 38.55 38.55 30.14 Lowest return –29.12 0.06 –7.06 Coefficient of skewness 0.42 4.28 2.84 Ignore for the moment the fourth column (“Perfect Timer—Fair Charge”). The results of rows one and two are self-explanatory. The third row, standard deviation, requires some 920 PART VII Active Portfolio Management 3 This demonstration has been extended to recent data with similar results. CONCEPT CHECK ☞ QUESTION 1 What was the monthly and annual compounded rate of return for the three strategies over the pe- riod 1926 to 1978? Bodie−Kane−Marcus: Investments, Fifth Edition VII. Active Portfolio Management 27. The Theory of Active Portfolio Management 924 © The McGraw−Hill Companies, 2001 CHAPTER 27 The Theory of Active Portfolio Management 921 discussion. The standard deviation of the rate of return earned by the perfect market timer was 3.82%, far greater than the volatility of T-bill returns over the same period. Does this imply that (perfect) timing is a riskier strategy than investing in bills? No. For this analysis standard deviation is a misleading measure of risk. To see why, consider how you might choose between two hypothetical strategies: The first offers a sure rate of return of 5%; the second strategy offers an uncertain return that is given by 5% plus a random number that is zero with probability .5 and 5% with probabil- ity .5. The characteristics of each strategy are Strategy 1 (%) Strategy 2 (%) Expected return 5 7.5 Standard deviation 0 2.5 Highest return 5 10.0 Lowest return 5 5.0 Clearly, Strategy 2 dominates Strategy 1 because its rate of return is at least equal to that of Strategy 1 and sometimes greater. No matter how risk averse you are, you will always prefer Strategy 2, despite its significant standard deviation. Compared to Strategy 1, Strat- egy 2 provides only “good surprises,” so the standard deviation in this case cannot be a measure of risk. These two strategies are analogous to the case of the perfect timer compared with an all- equity or all-bills strategy. In every period the perfect timer obtains at least as good a re- turn, in some cases a better one. Therefore the timer’s standard deviation is a misleading measure of risk compared to an all-equity or all-bills strategy. Returning to the empirical results, you can see that the highest rate of return is identical for the all-equity and the timing strategies, whereas the lowest rate of return is positive for the perfect timer and disastrous for all the all-equity portfolio. Another reflection of this is seen in the coefficient of skewness, which measures the asymmetry of the distribution of returns. Because the equity portfolio is almost (but not exactly) normally distributed, its coefficient of skewness is very low at .42. In contrast, the perfect timing strategy effectively eliminates the negative tail of the distribution of portfolio returns (the part below the risk-free rate). Its re- turns are “skewed to the right,” and its coefficient of skewness is therefore quite large, 4.28. Now for the fourth column, “Perfect Timer—Fair Charge,” which is perhaps the most in- teresting. Most assuredly, the perfect timer will charge clients for such a valuable service. (The perfect timer may have otherwordly predictive powers, but saintly benevolence is unlikely.) Subtracting a fair fee (discussed later) from the monthly rate of return of the timer’s portfolio gives us an average rate of return lower than that of the passive, all-equity strat- egy. However, because the fee is constructed to be fair, the two portfolios (the all-equity strategy and the market-timing-with-fee strategy) must be equally attractive after risk ad- justment. In this case, again, the standard deviation of the market timing strategy (with fee) is of no help in adjusting for risk because the coefficient of skewness remains high, 2.84. In other words, mean-variance analysis is inadequate for valuing market timing. We need an alternative approach. Valuing Market Timing as an Option The key to analyzing the pattern of returns to the perfect market timer is to recognize that perfect foresight is equivalent to holding a call option on the equity portfolio. The perfect [...]... do we generalize this rule to use in a multifactor model? To simplify, let us consider a two-factor world, and let us call the two factor portfolios M and H Then we generalize the index model to ri Ϫ rf ϭ ␤iM (rM Ϫ rf) ϩ ␤i H (rH Ϫ rf) ϩ ␣iϩ ei ϭ R␤ ϩ ␣iϩ ei (27.12) ␤iM and ␤iH are the betas of the security relative to portfolios M and H Given the rates of return on the factor portfolios, rM and rH,... two factor portfolios to construct its passive portfolio The input table that is constructed by the house analysts looks as follows: Micro Forecasts Asset Expected Return (%) Beta on M Beta on H Residual Standard Deviation (%) 20 18 17 12 1.2 1.4 0.5 1.0 1.8 1.1 1.5 0.2 58 71 60 55 Visit us at www.mhhe.com/bkm Stock A Stock B Stock C Stock D Macro Forecasts Asset T-bills Factor M portfolio Factor H... structure also suggests an efficient method to allocate research effort Analysts can specialize in forecasting means and variances of different factor portfolios Having established factor betas, they can form a covariance matrix to be used together with expected security returns generated by the CAPM or APT to construct an optimal passive Bodie−Kane−Marcus: Investments, Fifth Edition 932 VII Active Portfolio... variance to total variance ␳2 ϭ ␴2 ␣ 2 ␴␣ ϩ ␴2 ␧ This equation shows us how to “discount” analysts’ forecasts to reflect their precision Knowing the quality of past forecasts, ␳ 2, we “shrink” any new forecast, ␣ f, to ␳ 2␣ f, to minimize forecast error This procedure is quite intuitive: If the analyst is perfect, that is, ␳2 ϭ 1, we take the forecast at face value If analysts’ forecasts have proven to be... example, suppose the analyst covers three more stocks that turn out to have alphas and risk levels identical to the first three Use equation 27.9 to show that the squared appraisal ratio of the active portfolio will double By using equation 27.7, it is easy to show that the new Sharpe measure will rise to 5327 Equation 27.11 then implies that M 2 rises to 2.65%, almost double the previous value Increasing... various multifactor models of security returns So far our analytical framework for active portfolio management seems to rest on the validity of the index model, that is, on a single-factor security model Using a multifactor model will not affect the construction of the active portfolio because the entire TB analysis focuses on the residuals of the index model If we were to replace the one-factor model with... portfolio If active analysis of individual stocks also is attempted, the procedure of constructing the optimal active portfolio and its optimal combination with the passive portfolio is identical to that followed in the single-factor case In the case of the multifactor market even passive investors (meaning those who accept market prices as “fair”) need to do a considerable amount of work They need... Deviation (%) 8 16 10 0 23 18 The correlation coefficient between the two factor portfolios is 6 a What is the optimal passive portfolio? b By how much is the optimal passive portfolio superior to the single-factor passive portfolio, M, in terms of Sharpe’s measure? c Analyze the utility improvement to the A ϭ 2.8 investor relative to holding portfolio M as the sole risky asset that arises from the expanded... students, however, will benefit from some coaching to make the study of investment easier and more efficient If you had a good introductory quantitative methods course, and like the text that was used, you may want to refer to it whenever you feel in need of a refresher If you feel uncomfortable with standard quantitative texts, this reference is for you Our aim is to present the essential quantitative concepts... approach is structured in line with requirements for the CFA program The material included is relevant to investment management by the ICFA, the Institute of Chartered Financial Analysts We hope you find this appendix helpful Use it to make your venture into investments more enjoyable 940 Bodie−Kane−Marcus: Investments, Fifth Edition Back Matter Appendix A: Quantitative Review APPENDIX A Quantitative Review . this rule to use in a multifactor model? To simplify, let us con- sider a two-factor world, and let us call the two factor portfolios M and H. Then we gener- alize the index model to r i Ϫ r f ϭ␤ iM (r M Ϫ. motives: To mitigate the large risk of individual stocks (verify that the stan- dard deviation of stock 1 is 55%) and maximize the portfolio Sharpe measure (which com- pares excess return to total. index model. If we were to replace the one-factor model with a multifactor model, we would continue to form the active portfolio by calculating each security’s alpha relative to its fair return (given